As somebody with sites using all three tiers of their service, I haven't noticed a speed difference between any of the tiers.

I've had that experience (with Cloudflare in general, not DNS). My average response times as measured by Google webmaster tools went from 30ms to 300ms, if I remember correctly. This way ~18 months ago though, so I don't know if it has changed.

And it's to be expected to be slightly slower, at least for dynamic requests, since it's a reverse proxy. I doubt it's limited to the free tier.

I've used the DNS for a few years without any issues whatsoever, so I'd recommend them for that.

You can use Cloudflare to manage DNS only, so there is no "slow down".